Stockfish NNUE

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Stockfish NNUE Logo [1]

Stockfish NNUE,
a Stockfish branch by Hisayori Noda aka Nodchip, which uses Efficiently Updatable Neural Networks - stylized as ƎUИИ or reversed as NNUE - to replace its standard evaluation. NNUE, introduced in 2018 by Yu Nasu [2], were previously successfully applied in Shogi evaluation functions embedded in a Stockfish based search [3], such as YaneuraOu [4], and Kristallweizen [5]. YaneuraOu's author Motohiro Isozaki made an unbelievable prediction that NNUE can help to increase Stockfish strength by around 100 points, almost one year before revealing [6] [7]. In 2019, Nodchip incorporated NNUE into Stockfish 10 - as a proof of concept, and with the intention to give something back to the Stockfish community [8]. After support and announcements by Henk Drost in May 2020 [9] and subsequent enhancements, Stockfish NNUE was established and recognized. In summer 2020, with more people involved in testing and training, the computer chess community bursts out enthusiastically due to its rapidly raising playing strength with different networks trained using a mixture of supervised and reinforcement learning methods. Despite the approximately halved search speed, Stockfish NNUE became stronger than its original [10].

In August 2020, Fishtest revealed Stockfish NNUE was stronger than the classical one at least 80 Elo [11]. In July 2020, the playing code of NNUE was put into the official Stockfish repository as a branch for further development and examination. In August that playing code merged to the master branch and become an official part of the engine. However, the training code still remained in Nodchip's repository [12] [13]. On September 02, 2020, Stockfish 12 was released with a huge jump in playing strength due to the introduction of NNUE and further tuning [14].

NNUE Structure

The neural network consists of four layers. The input layer is heavily overparametrized, feeding in the board representation for all king placements per side [15].

The so called HalfKP structure consists of two halves covering input layer and first hidden layer, each half of the input layer associated to one of the two kings, cross coupled with the side to move or not to move halves of the first hidden layer. For each either black or white king placement, the 10 none king pieces on their particular squares are the boolean {0,1} inputs, along with a relict from Shogi piece drop (BONA_PIECE_ZERO), 64 x (64 x 10 + 1) = 41,024 inputs for each half, which are multiplied by a 16-bit integer weight vector for 256 outputs per half, in total, 256 x 41,024 = 10,502,144 weights. As emphasized by Ronald de Man in a CCC forum discussion [16], the input weights are arranged in such a way, that color flipped king-piece configurations in both halves share the same index. However, and that seems also a relict from Shogi with its 180 degrees rotational 9x9 board symmetry, instead of vertical flipping (xor 56), rotation is applied (xor 63) [17].

The efficiency of NNUE is due to incremental update of the input layer outputs in make and unmake move, where only a tiny fraction of its neurons need to be considered in case of none king moves. The remaining three layers with 2x256x32, 32x32 and 32x1 weights are computational less expensive, hidden layers apply a ReLu activation [18] [19], best calculated using appropriate SIMD instructions performing fast 8-bit/16-bit integer vector arithmetic, like MMX, SSE2 or AVX2 on x86/x86-64, or, if available, AVX-512.


NNUE layers in action [20]

Explanation by Ronald de Man [21], who did the Stockfish NNUE port to CFish [22]:

The accumulator has a "white king" half and a "black king" half, where each half is a 256-element vector of 16-bit ints, which is equal to the sum of the weights of the "active" (pt, sq, ksq) features  plus a 256-element vector of 16-bit biases.
The "transform" step of the NNUE evaluation forms a 512-element vector of 8-bit ints where the first half is formed from the 256-element vector of the side to move and the second half is formed from the 256-element vector of the other side. In this step the 16-bit elements are clipped/clamped to a value from 0 to 127. This is the output of the input layer.
This 512-element vector of 8-bit ints is then multiplied by a 32x512 matrix of 8-bit weights to get a 32-element vector of 32-bit ints, to which a vector of 32-bit biases is added. The sum vector is divided by 64 and clipped/clamped to a 32-element vector of 8-bit ints from 0 to 127. This is the output of the first hidden layer.
The resulting 32-element vector of 8-bit ints is multiplied by a 32x32 matrix of 8-bit weights to get a 32-element vector of 32-bit ints, to which another vector of 32-bit biases is added. These ints are again divided by 64 and clipped/clamped to 32 8-bit ints from 0 to 127. This is the output of the second hidden layer.
This 32-element vector of 8-bits ints is then multiplied by a 1x32 matrix of 8-bit weights (i.e. the inner product of two vectors is taken). This produces a 32-bit value to which a 32-bit bias is added. This gives the output of the output layer.
The output of the output layer is divided by FV_SCALE = 16 to produce the NNUE evaluation. SF's evaluation then take some further steps such as adding a Tempo bonus (even though the NNUE evaluation inherently already takes into account the side to move in the "transform" step) and scaling the evaluation towards zero as rule50_count() approaches 50 moves.


All networks are built by some volunteers but not by any big community (differs from Leela Chess Zero) and can be uploaded into Fishtest for testing. Networks with good test results will be released officially on Fishtest website [23].

After long discussing the best way to publish networks with Stockfish [24], the developing team decided to embed the default network into Stockfish binaries, making sure NNUE always works as well as bringing more convenience to users.


In August 2020 a new patch changed Stockfish NNUE into a hybrid engine: it uses NNUE evaluation only on quite balanced material positions, otherwise uses the classical one. It could speed up to 10% and gain 20 Elo [25]. At that point, NNUE helped to increase already around 100 Elo for Stockfish. In the same month, Stockfish changed the default mode of using evaluation functions from classic to hybrid one, the last step to completely accept NNUE.

Strong Points

For Users

  • Runs with CPU only, and doesn't require expensive video cards, as well the need for installing drivers and 3rd specific libraries. Thus it is much easier to install (compared to engines using deep convolutional neural networks, such as Leela Chess Zero) and suitable for almost all modern computers. Using a GPU is even not practical for that small net - host-device-latency aka. kernel-launch-overhead [26] [27] to a then underemployed GPU are not sufficient for the intended NPS range [28]
  • Releases with only one network (via UCI options), that help to delete users' confusion from finding, selecting and setting up. The network is selected carefully from Fishtest

For Developers

  • Requires small training sets. Some high score networks can be built with the effort of one or a few people within a few days. It doesn't require the massive computing from a supercomputer and/or from community
  • Doesn’t require complicated systems such as a sophisticated client-server model to train networks. Just a single binary from Nodchip’ repo is enough to train
  • The NNUE code is independent and can be separated easily from the rest and integrated to other engines [29]

Being attracted by new advantages as well as being encouraged by some impressive successes, many developers joined or continued to work. The Official Stockfish repository shows the numbers of commits, ideas increased significantly after merging NNUE.


In reply to Unai Corzo, Motohiro Isozaki aka Yaneurao, suggested 3 techniques that applied successfully to Shogi and can be brought back to Stockfish NNUE and may improve it another 100 - 200 Elo [30] [31]:

See also

Forum Posts

2020 ...

January ...


Re: NNUE accessible explanation by Jonathan Rosenthal, CCC, July 23, 2020
Re: NNUE accessible explanation by Jonathan Rosenthal, CCC, July 24, 2020
Re: NNUE accessible explanation by Jonathan Rosenthal, CCC, August 03, 2020


Re: this will be the merge of a lifetime : SF 80 Elo+ by Henk Drost, CCC, August 04, 2020



Re: NNUE Question - King Placements by syzygy, CCC, October 23, 2020
Re: NNUE Question - King Placements by syzygy, CCC, October 23, 2020

2021 ...

External Links







  1. Stockfish NNUE Logo from GitHub - nodchip/Stockfish: UCI chess engine by Nodchip
  2. Yu Nasu (2018). ƎUИИ Efficiently Updatable Neural-Network based Evaluation Functions for Computer Shogi. Ziosoft Computer Shogi Club, pdf (Japanese with English abstract) GitHub - asdfjkl/nnue translation
  3. The Stockfish of shogi by Larry Kaufman, CCC, January 07, 2020
  4. GitHub - yaneurao/YaneuraOu: YaneuraOu is the World's Strongest Shogi engine(AI player), WCSC29 1st winner, educational and USI compliant engine
  5. GitHub - Tama4649/Kristallweizen: 第29回世界コンピュータ将棋選手権 準優勝のKristallweizenです。
  6. 将棋ソフト開発者がStockfishに貢献する日 The day when shogi software developers contribute to Stockfish by Motohiro Isozaki, June 2019
  7. shogi engine developer claims he can make Stockfish stronger, Reddit, August 2019
  8. Stockfish NNUE – The Complete Guide, June 19, 2020 (Japanese and English)
  9. Stockfish NN release (NNUE) by Henk Drost, CCC, May 31, 2020
  10. Can the sardine! NNUE clobbers SF by Henk Drost, CCC, July 16, 2020
  11. Introducing NNUE Evaluation, August 06, 2020
  12. NNUE merge · Issue #2823 · official-stockfish/Stockfish · GitHub by Joost VandeVondele, July 25, 2020
  13. GitHub - nodchip/Stockfish: UCI chess engine by Nodchip
  14. Stockfish 12, The Stockfish Team, Stockfish Blog, September 02, 2020
  15. Re: NNUE accessible explanation by Jonathan Rosenthal, CCC, July 23, 2020
  16. Re: NNUE Question - King Placements by syzygy, CCC, October 23, 2020
  17. NNUE eval rotate vs mirror · Issue #3021 · official-stockfish/Stockfish · GitHub by Terje Kirstihagen, August 17, 2020
  18. Stockfish/halfkp_256x2-32-32.h at master · official-stockfish/Stockfish · GitHub
  19. Stockfish/clipped_relu.h at master · official-stockfish/Stockfish · GitHub
  20. Image courtesy Roman Zhukov, revised version of the image posted in Re: Stockfish NN release (NNUE) by Roman Zhukov, CCC, June 17, 2020, labels corrected October 23, 2020, see Re: NNUE Question - King Placements by Andrew Grant, CCC, October 23, 2020
  21. Re: NNUE Question - King Placements by syzygy, CCC, October 23, 2020
  22. Cfish/nnue.c at master · syzygy1/Cfish · GitHub
  23. Neural Net download and statistics
  24. Improve dealing with the default net? Issue ##3030 · official-stockfish/Stockfish · GitHub by Joost VandeVondele, August 19, 2020
  25. NNUE evaluation threshold by MJZ1977 · Pull Request #2916 · official-stockfish/Stockfish · GitHub, August 06, 2020
  26. AB search with NN on GPU... by Srdja Matovic, CCC, August 13, 2020 » GPU
  27. kernel launch latency - CUDA / CUDA Programming and Performance - NVIDIA Developer Forums by LukeCuda, June 18, 2018
  28. stockfish with graphics card by h1a8, CCC, August 06, 2020
  29. NNUE Engines
  30. 3 technologies in shogi AI that could be used for chess AI, Motohiro Isozaki, August 2020
  31. GitHub - NNUE ideas and discussion (post-merge). #2915, August 2020
  32. Update default net to nn-8a08400ed089.nnue by Sopel97 · Pull Request #3474 · official-stockfish/Stockfish · GitHub by Tomasz Sobczyk
  33. An info by Sylwy, CCC, July 25, 2020
  34. You can now look inside NNUE and look at its Per square value estimation by Henk Drost, CCC, August 04, 2020

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